Q1: Does this card's inherited effect also activate if a single effect such as "Draw 1. Then, trash 1 card in the hand" trashes the same number of cards as the number that were added from the draw?
Yes, it activates.
Q2: Does this card's inherited effect activate when the hand increases from the digivolution bonus upon digivolution by an effect?
No, it doesn’t activate.
Koji Minamoto BT17-083 R [Security] Play this card without paying the cost. [Start of Your Turn] If you have 2 or less memory, set it to 3.
Koji Minamoto BT17-083 R [Security] Play this card without paying the cost. [Start of Your Turn] If you have 2 or less memory, set it to 3. --- [Your Turn] [Once Per Turn] When an effect adds cards to your hand, gain 1 memory. Then, this Digimon gains <Jamming> for the turn.
Koji Minamoto BT17-083 R [Security] Play this card without paying the cost. [Start of Your Turn] If you have 2 or less memory, set it to 3. --- [Your Turn] [Once Per Turn] When an effect adds cards to your hand, gain 1 memory. Then, this Digimon gains <Jamming> for the turn.
源輝二 BT17-083 R 【セキュリティ】このカードをコストを支払わずに登場させる。 【自分のターン開始時】メモリーが2以下なら、3にする。 --- 【自分のターン】[ターンに1回]効果で自分の手札が増えたとき、メモリー+1。その後、ターン終了まで、このデジモンは≪ジャミング≫を得る。